Hi Michelle,

Q1. Complete the Square for x^2 - 9x + r

(Try it yourself while I fill this space with anti-spoilers)

It becomes (x-4.5)^2 + (r-20.25),
where the x,y coordinates of the minimum point are (4.5 , r-20.25).

r - 20.25 = -9.25, hence r = 11


Q2. If 3 points P, Q and R are collinear, then it should make sense that the gradients of line segments PQ, PR, and QR are the same.

(Use the gradient of straight line formula to construct expressions for any 2 line segments of your choice, then equate the 2 gradient expressions together and solve for q)
(formula is (y2 - y1) / (x2 - x1) )
(anti-spoilers filling this space)

My sample answer:

gradient of PR = (4 - -5)/(3+q- -2) = (9)/(5+q)
gradient of QR = (q - -5)/(2 - -2) = (q+5)/(4)

equating gradients:
(9)/(5+q) = (q+5)/(4)

cross multiply:
36 = (q+5)^2
q+5 = +6 or q+5 = -6
q = 1 or q = -11